Understand the concept of a regression. A regression is a mathematical formula to try to predict something based off of relationships with other factors. This is often done to try to explain what causes or is likely to cause something else to happen. For example, you might want to try to predict a college GPA based on drinking or sleep habits.
Understand the independent variable, aka the y variable or the variable on the left side of the equals sign. This is normally written in words. It would be something like student test scores, points scored in the game, height... These are things that were measured in the study. What the regression is aiming to do is predict this variable.
Look at the dependent variables, aka the x variable or the variable on the right side of the equals sign. There may be one variable in the simplest of models, and there may be several variables in more complex regressions. These variables were also measured in the study and the researchers are using these variables to try to predict the independent variable. Some of these variables are numbers and others are yes/no variables, so be sure you understand how each is measured. The paper will explain this.
Identify the coefficients. These will most likely be listed in a table where the dependent variables are listed vertically and there are several combination of models where there is a coefficient listed in columns. If there is a number listed in that column, then that variable was included in the model.
Interpret the coefficients. Each number on the coefficient means that if there is a one unit increase in the dependent variable, there is that much change in the independent variable. For example, if the model was SAT scores= male + GPA and the coefficients were 100 for male and 300 for GPA, then male's SAT score would be 100 points higher, on average, than females. Similarly, for a 1 point increase in GPA (from a 3.0 to 4.0) there would be a 300 point increase in a person's SAT score.
Interpret the intercept. Some papers will give the intercept of the model, and this is the only way that you can actually predict the value of scores for people. For example, if the model was: SAT scores= 1000 + 100 male + 300 GPA, a female with a GPA of 3.5 would have a score of 2050.
Look for the stars on each of the coefficients. Stars indicated if a model is statistically significant. Even if you don't fully understand what that means, know that stars are required to interpret the model. If a model does not have stars, it generally is not a good model.
Think about the big picture. Does it make sense to use this model? Is there any other variables that might be missing? Do you see any flaws in the methodology. You aren't expected to be an expert, but be sure to really think about if the model makes sense and in a good fit.